To prepare the potatoes, peel and cut into roughly 2.5cm/1in chunks. Put the potatoes in a pan and cover with cold water. Bring to the boil, reduce the heat slightly and simmer for five minutes.
Drain the potatoes in a colander and leave to stand for two minutes. Bash up the edges of the potatoes a little by shaking the colander from side to side. This will help make them extra crisp.
Melt the butter with the oil in a large non-stick frying pan or sauté pan. Tip the potatoes into the pan and season with salt and plenty of freshly ground black pepper. Fry over a medium-low heat for 10 minutes, stirring occasionally.
Open out the garlic bulb and remove the cloves. Scatter the unpeeled garlic cloves into the pan with the potatoes and cook for 15 minutes, turning regularly until the potatoes are golden-brown all over and the garlic has softened. Sprinkle over the thyme leaves and cook for five minutes more, stirring and turning the potatoes as before. Once the thyme has been added to the potatoes, the steaks can be cooked.
For the steak, put the peppercorns in a pestle and mortar and pound until coarsely ground. Add the sea salt and mix lightly. Put the steaks on a board and season well on both sides with the pepper and salt mixture until lightly but evenly crusted.
Melt the butter with the oil in a large non-stick frying pan and fry the steaks over a medium high heat for 2-2½ minutes on each side for rare steak. Cook for 1-2 minutes longer on each side if prefer your steaks medium-rare and up to three minutes longer for medium, depending on thickness. Remove the steaks from the pan and place on warmed plates to rest while the sauce is prepared.
Add the finely sliced shallot to the frying pan and cook for 2-3 minutes, stirring until softened and lightly browned. Pour the brandy into the pan and sizzle for a few seconds. With great care, take a lit match and carefully light the brandy. Stand back well away from the flame in the pan. (If you prefer not to light the flame, simply cook the brandy for about 15 seconds before adding the other ingredients.)
When the flames have disappeared, add the mustard and Worcestershire sauce to the pan, stirring constantly. Pour over the stock and bring to the boil. Cook for 1-2 minutes, or until the volume of liquid has reduced by nearly half, stirring regularly.
Stir in the double cream and return the sauce to a simmer, stirring. Continue to simmer and stir until the sauce is thick enough to lightly coat the back of your spoon. Season to taste and stir through the tarragon, if using.
Spoon the sauce over the warm steaks and serve with the sauté potatoes and a crisp mixed salad. Squeeze the garlic out of its skins when you eat it.